Conic Sections is one of the most fundamental chapters in Class 11 Mathematics, forming the base for coordinate geometry and several advanced topics in higher classes. The uploaded PDF is a well-structured study resource for Chapter 12 – Conic Sections, covering circles, ellipse, parabola, and hyperbola along with their definitions, standard equations, properties, and important formulas. It presents concepts in a systematic way, supported by diagrams and step-by-step explanations, making it easier for students to grasp both theory and application.
I am writing about this PDF because many Class 11 students struggle to organise their preparation for Conic Sections due to the large number of formulas and variations of equations involved. This document brings all essential concepts together in one place, helping students revise faster and practise smarter. Whether you are preparing for school exams, competitive exams, or just strengthening your basics, understanding what this PDF offers can save time and improve accuracy. CLASS 11 – CONIC SECTION
Overview of Chapter 12 – Conic Sections
The PDF is divided into two parts and begins with chapter objectives. It explains how different conic sections are obtained by cutting a cone at various angles and positions. It also introduces degenerated cases such as a point, straight line, and pair of intersecting lines.
The main sections covered are:
- Circle
- Ellipse
- Parabola
- Hyperbola
Each section includes definitions, standard equations, properties, parametric forms, and equations of tangent and normal.
Concept of Section of a Cone
The PDF explains that when a right circular cone is cut by a plane, different curves are obtained depending on the angle and position of the plane.
- Parallel to base → Circle
- Inclined but not cutting base → Ellipse
- Parallel to generator → Parabola
- Cutting both nappes → Hyperbola
This geometric idea forms the foundation of the entire chapter.
Circle – Definitions and Standard Forms
A circle is defined as the locus of a point whose distance from a fixed point (centre) is always constant.
Standard equation of a circle with centre (h, k):
(x – h)² + (y – k)² = r²
Important cases discussed in the PDF include:
- Circle with centre at origin
- Circle passing through origin
- Circle touching x-axis or y-axis
- Circle touching both axes
- Circle passing through two endpoints of a diameter
- Circle passing through three non-collinear points
The PDF also gives the general equation of a circle:
x² + y² + 2gx + 2fy + c = 0
Centre = (–g, –f)
Radius = √(g² + f² – c)
Tangent and Normal to a Circle
The document explains formulas for:
- Equation of tangent at a point
- Tangent in slope form
- Equation of normal at a given point
These formulas are extremely important for board exams and competitive tests.
Properties of a Circle
Some key properties included are:
- Tangent is perpendicular to radius at point of contact
- Equal chords are equidistant from centre
- Diameter is the longest chord
- Two tangents from an external point are equal
Ellipse – Definition and Standard Equation
An ellipse is the locus of a point such that the ratio of its distance from a focus to its distance from a directrix is constant and less than one.
Standard equation:
x²/a² + y²/b² = 1
The PDF explains:
- Vertices and foci
- Major and minor axes
- Eccentricity
- Directrices
- Latus rectum
Parametric form:
x = a cosθ
y = b sinθ
Tangent and Normal to an Ellipse
The PDF provides:
- Condition for a line to be tangent
- Equation of tangent at a point
- Tangent in slope form
- Normal in point, slope, and parametric forms
Download this CLASS 11 – CONIC SECTION PDF File: Click Here
Parabola – Definition and Basic Forms
A parabola is the locus of a point whose distance from a fixed point (focus) equals its distance from a fixed line (directrix).
Standard equation:
y² = 4ax
Other forms:
- (y – k)² = 4a(x – h)
- (x – h)² = 4a(y – k)
The PDF also discusses vertex, axis, latus rectum, focal chord, and double ordinate.
Tangent and Normal to a Parabola
Formulas included:
- Point form of tangent
- Slope form of tangent
- Parametric form of tangent
- Equation of normal in point, slope, and parametric forms
Hyperbola – Definition and Standard Equation
A hyperbola is the locus of a point such that the ratio of its distance from a focus to its distance from a directrix is constant and greater than one.
Standard equation:
x²/a² – y²/b² = 1
The PDF explains vertices, foci, directrices, eccentricity, latus rectum, and asymptotes.
Parametric form:
x = a secθ
y = b tanθ
Tangent, Normal, and Asymptotes of Hyperbola
Students will find:
- Condition for tangency
- Equation of tangent in slope, point, and parametric forms
- Equation of normal in different forms
- Equations of asymptotes
- Rectangular hyperbola and its equation xy = c²
Important Formulae Section
At the end, the PDF provides a consolidated list of important formulas for circle, ellipse, parabola, and hyperbola. This section is extremely useful for last-minute revision.
Who Should Use This PDF
- Class 11 Mathematics students
- Students preparing for Class 12 in advance
- JEE and other competitive exam aspirants
- Anyone wanting strong fundamentals in coordinate geometry
